You did not mention the reason for the impoundment of your vehicle. If it was for a serious violation such as driving without insurance or without a license then having your license suspended and /or imprisonment are likely penalties.

Alaska has a Mandatory Insurance Law which requires either the vehicle owner or driver to carry liability insurance. The minimum amount of liability insurance coverage is $50,000/$100,000 for bodily injury or death and $25,000 for property damage. You must carry proof of liability insurance in your vehicle. Failure to provide proof of liability insurance to a law enforcement officer may result in a traffic citation or the vehicle may be impounded.

If you are involved in a crash, which results in bodily injury or death to a person, or property damage in excess of $501, you must provide, within 15 days, proof of insurance to the AK Division of Motor Vehicles. If you were uninsured or you fail to provide the proof within 15 days, your driver’s license will be suspended for 90 days for a first occurrence and 1 year for a second occurrence.

Alaska Statute section 28.22.019 is about proof of insurance to be carried and exhibited on demand. Subsection a states that a person shall have proof of motor vehicle liability insurance in the person's immediate possession at all times when driving a motor vehicle, and shall present the proof for inspection upon the demand of a peace officer or other authorized representative of the Department of Public Safety.

This Statute goes on to say that a municipality may impose a penalty for violating the ordinance as provided under AS 29.25.070. Section 29.25.070 states that:

(a) For the violation of an ordinance, a municipality may by ordinance prescribe a penalty not to exceed a fine of $1,000 and imprisonment for 90 days. For a violation that cannot result in incarceration or the loss of a valuable license, a municipality may allow disposition of the violation without court appearance and establish a schedule of fine amounts for each offense.

If instead you were cited and convicted of an offense such as driving while your driver's license is cancelled, suspended, revoked, or in violation of a limited license then it can result in a jail sentence of not less than 10 days.

Whatever offense you were cited for in Alaska that resulted in your car being impounded for a second time, you should check with the court listed on your ticket to find out what penalties you may receive and if jail or imprisonment for a certain number of days is a possibility.